Do you think using say 5/8 plywood instead of 3/4 would be sturdy
enough? Since LCD's are much lighter than crt's I would think the
thinner would be ok. The only drawback i see right now would be
t-molding and if I could find some to work on 5/8 instead of 3/4.
I think 5/8 plywood could work. My cabinet is pretty stable, but it has the slightest flex in it. Sometimes the front lower access door (where the coin box is) seems to be bound a little when I try to open it (which isn't often). I made that door fairly tight (very little gap).
I think with 5/8" you may need better/smarter cross-bracing than I used. I built my cabinet so it could be completely disassembled. I think if I had glued and screwed it all together in a permanent structure it would have made a big difference. Again, mine isn't flimsy in the least, but I sense there is has the slightest flex because of that front door (haven't noticed any other flex problems).
You definitely need the T-molding to fit that size. That T-molding website has tons of choices, so they may have what you need.